+0  
 
+2
440
1
avatar+75 

Let $AB = 6$, $BC = 8$, and $AC = 10$. What is the area of the circumcircle of $\triangle ABC$ minus the area of the incircle of $\triangle ABC$?

eileenthecoolbean  Jul 14, 2017
 #1
avatar+87564 
+1

 

 The radius of the cicumscribing circle is given by :

 

[ Product of the side lengrhs ]  /  [ 4 * Area of the triangle ]  =

 

[ 6 * 8 * 10 ] / [ 4 (1/2) * 6 * 8]  =    10 / 2  =  5 units

 

The radius of the incircle is given by 

 

[ 2*Area of the triangle] / [Perimeter]  = [ 2* (1/2) * 6 * 8] / [ 6 + 8 + 10]  = 48 / 24  = 2 units

 

So....the area of the circumcircle - area of the incircle  =

 

[pi] [5^2 - 2^2] =  pi * [25 - 4] = 21pi  units^2 ≈ 65.97 units^2

 

 

cool cool cool

CPhill  Jul 14, 2017

19 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.